Many people have experiences that trigger the belief that reality is a cold and uncaring place, indifferent to their welfare. Such belief-triggering experiences are surprising on theism, since on that hypothesis, we'd expect God to design our cognitive faculties in such a way as to reliably trigger true beliefs about reality, according to which (on that hypothesis) reality is not a cold and uncaring place that is indifferent to our welfare. By contrast, such belief-triggering experiences are not surprising on naturalism, since on that hypothesis, reality really is a cold and uncaring place that is indifferent to our welfare. Therefore, the existence and pervasiveness of anti-religious experience provides at least some confirming evidence for naturalism vis-a-vis theism.
Update: I've been reminded that a version of this sort of argument has been carefully developed and defended by Sarah Adams and John Robson in their excellent paper, "Does absence make atheistic belief grow stronger?", International Journal for Philosophy of Religion 79 (2016), pp. 49-69. Thanks to Kaspian for the reminder.